1 /***************************************************************************/
5 /* FreeType trigonometric functions (body). */
7 /* Copyright 2001, 2002, 2003, 2004, 2005 by */
8 /* David Turner, Robert Wilhelm, and Werner Lemberg. */
10 /* This file is part of the FreeType project, and may only be used, */
11 /* modified, and distributed under the terms of the FreeType project */
12 /* license, LICENSE.TXT. By continuing to use, modify, or distribute */
13 /* this file you indicate that you have read the license and */
14 /* understand and accept it fully. */
16 /***************************************************************************/
20 #include FT_INTERNAL_OBJECTS_H
21 #include FT_TRIGONOMETRY_H
24 /* the following is 0.2715717684432231 * 2^30 */
25 #define FT_TRIG_COSCALE 0x11616E8EUL
27 /* this table was generated for FT_PI = 180L << 16, i.e. degrees */
28 #define FT_TRIG_MAX_ITERS 23
31 ft_trig_arctan_table[24] =
33 4157273L, 2949120L, 1740967L, 919879L, 466945L, 234379L, 117304L,
34 58666L, 29335L, 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L,
35 57L, 29L, 14L, 7L, 4L, 2L, 1L
38 /* the Cordic shrink factor, multiplied by 2^32 */
39 #define FT_TRIG_SCALE 1166391785UL /* 0x4585BA38UL */
42 #ifdef FT_CONFIG_HAS_INT64
44 /* multiply a given value by the CORDIC shrink factor */
46 ft_trig_downscale( FT_Fixed val )
53 val = ( val >= 0 ) ? val : -val;
55 v = ( val * (FT_Int64)FT_TRIG_SCALE ) + 0x100000000UL;
56 val = (FT_Fixed)( v >> 32 );
58 return ( s >= 0 ) ? val : -val;
61 #else /* !FT_CONFIG_HAS_INT64 */
63 /* multiply a given value by the CORDIC shrink factor */
65 ft_trig_downscale( FT_Fixed val )
68 FT_UInt32 v1, v2, k1, k2, hi, lo1, lo2, lo3;
72 val = ( val >= 0 ) ? val : -val;
74 v1 = (FT_UInt32)val >> 16;
75 v2 = (FT_UInt32)(val & 0xFFFFL);
77 k1 = (FT_UInt32)FT_TRIG_SCALE >> 16; /* constant */
78 k2 = (FT_UInt32)(FT_TRIG_SCALE & 0xFFFFL); /* constant */
81 lo1 = k1 * v2 + k2 * v1; /* can't overflow */
83 lo2 = ( k2 * v2 ) >> 16;
84 lo3 = ( lo1 >= lo2 ) ? lo1 : lo2;
89 hi += (FT_UInt32)0x10000UL;
93 return ( s >= 0 ) ? val : -val;
96 #endif /* !FT_CONFIG_HAS_INT64 */
100 ft_trig_prenorm( FT_Vector* vec )
109 z = ( ( x >= 0 ) ? x : - x ) | ( (y >= 0) ? y : -y );
113 /* determine msb bit index in `shift' */
114 if ( z >= ( 1L << 16 ) )
119 if ( z >= ( 1L << 8 ) )
124 if ( z >= ( 1L << 4 ) )
129 if ( z >= ( 1L << 2 ) )
134 if ( z >= ( 1L << 1 ) )
156 if ( z < ( 1L << 27 ) )
162 } while ( z < ( 1L << 27 ) );
166 else if ( z > ( 1L << 28 ) )
172 } while ( z > ( 1L << 28 ) );
186 ft_trig_pseudo_rotate( FT_Vector* vec,
190 FT_Fixed x, y, xtemp;
191 const FT_Fixed *arctanptr;
197 /* Get angle between -90 and 90 degrees */
198 while ( theta <= -FT_ANGLE_PI2 )
202 theta += FT_ANGLE_PI;
205 while ( theta > FT_ANGLE_PI2 )
209 theta -= FT_ANGLE_PI;
212 /* Initial pseudorotation, with left shift */
213 arctanptr = ft_trig_arctan_table;
217 xtemp = x + ( y << 1 );
220 theta += *arctanptr++;
224 xtemp = x - ( y << 1 );
227 theta -= *arctanptr++;
230 /* Subsequent pseudorotations, with right shifts */
236 xtemp = x + ( y >> i );
239 theta += *arctanptr++;
243 xtemp = x - ( y >> i );
246 theta -= *arctanptr++;
248 } while ( ++i < FT_TRIG_MAX_ITERS );
256 ft_trig_pseudo_polarize( FT_Vector* vec )
261 const FT_Fixed *arctanptr;
267 /* Get the vector into the right half plane */
273 theta = 2 * FT_ANGLE_PI2;
279 arctanptr = ft_trig_arctan_table;
283 /* Rotate positive */
287 theta -= *arctanptr++; /* Subtract angle */
291 /* Rotate negative */
295 theta += *arctanptr++; /* Add angle */
303 /* Rotate positive */
307 theta -= *arctanptr++;
311 /* Rotate negative */
315 theta += *arctanptr++;
317 } while ( ++i < FT_TRIG_MAX_ITERS );
321 theta = FT_PAD_ROUND( theta, 32 );
323 theta = -FT_PAD_ROUND( -theta, 32 );
330 /* documentation is in fttrigon.h */
332 FT_EXPORT_DEF( FT_Fixed )
333 FT_Cos( FT_Angle angle )
338 v.x = FT_TRIG_COSCALE >> 2;
340 ft_trig_pseudo_rotate( &v, angle );
342 return v.x / ( 1 << 12 );
346 /* documentation is in fttrigon.h */
348 FT_EXPORT_DEF( FT_Fixed )
349 FT_Sin( FT_Angle angle )
351 return FT_Cos( FT_ANGLE_PI2 - angle );
355 /* documentation is in fttrigon.h */
357 FT_EXPORT_DEF( FT_Fixed )
358 FT_Tan( FT_Angle angle )
363 v.x = FT_TRIG_COSCALE >> 2;
365 ft_trig_pseudo_rotate( &v, angle );
367 return FT_DivFix( v.y, v.x );
371 /* documentation is in fttrigon.h */
373 FT_EXPORT_DEF( FT_Angle )
374 FT_Atan2( FT_Fixed dx,
380 if ( dx == 0 && dy == 0 )
385 ft_trig_prenorm( &v );
386 ft_trig_pseudo_polarize( &v );
392 /* documentation is in fttrigon.h */
394 FT_EXPORT_DEF( void )
395 FT_Vector_Unit( FT_Vector* vec,
398 vec->x = FT_TRIG_COSCALE >> 2;
400 ft_trig_pseudo_rotate( vec, angle );
406 /* these macros return 0 for positive numbers,
407 and -1 for negative ones */
408 #define FT_SIGN_LONG( x ) ( (x) >> ( FT_SIZEOF_LONG * 8 - 1 ) )
409 #define FT_SIGN_INT( x ) ( (x) >> ( FT_SIZEOF_INT * 8 - 1 ) )
410 #define FT_SIGN_INT32( x ) ( (x) >> 31 )
411 #define FT_SIGN_INT16( x ) ( (x) >> 15 )
414 /* documentation is in fttrigon.h */
416 FT_EXPORT_DEF( void )
417 FT_Vector_Rotate( FT_Vector* vec,
427 if ( angle && ( v.x != 0 || v.y != 0 ) )
429 shift = ft_trig_prenorm( &v );
430 ft_trig_pseudo_rotate( &v, angle );
431 v.x = ft_trig_downscale( v.x );
432 v.y = ft_trig_downscale( v.y );
436 FT_Int32 half = (FT_Int32)1L << ( shift - 1 );
439 vec->x = ( v.x + half + FT_SIGN_LONG( v.x ) ) >> shift;
440 vec->y = ( v.y + half + FT_SIGN_LONG( v.y ) ) >> shift;
445 vec->x = v.x << shift;
446 vec->y = v.y << shift;
452 /* documentation is in fttrigon.h */
454 FT_EXPORT_DEF( FT_Fixed )
455 FT_Vector_Length( FT_Vector* vec )
463 /* handle trivial cases */
466 return ( v.y >= 0 ) ? v.y : -v.y;
470 return ( v.x >= 0 ) ? v.x : -v.x;
474 shift = ft_trig_prenorm( &v );
475 ft_trig_pseudo_polarize( &v );
477 v.x = ft_trig_downscale( v.x );
480 return ( v.x + ( 1 << ( shift - 1 ) ) ) >> shift;
482 return v.x << -shift;
486 /* documentation is in fttrigon.h */
488 FT_EXPORT_DEF( void )
489 FT_Vector_Polarize( FT_Vector* vec,
499 if ( v.x == 0 && v.y == 0 )
502 shift = ft_trig_prenorm( &v );
503 ft_trig_pseudo_polarize( &v );
505 v.x = ft_trig_downscale( v.x );
507 *length = ( shift >= 0 ) ? ( v.x >> shift ) : ( v.x << -shift );
512 /* documentation is in fttrigon.h */
514 FT_EXPORT_DEF( void )
515 FT_Vector_From_Polar( FT_Vector* vec,
522 FT_Vector_Rotate( vec, angle );
526 /* documentation is in fttrigon.h */
528 FT_EXPORT_DEF( FT_Angle )
529 FT_Angle_Diff( FT_Angle angle1,
532 FT_Angle delta = angle2 - angle1;
535 delta %= FT_ANGLE_2PI;
537 delta += FT_ANGLE_2PI;
539 if ( delta > FT_ANGLE_PI )
540 delta -= FT_ANGLE_2PI;